Magnesium alkyls are used as homogenous catalysts in the production of linear low-density polyethylene (LLDPE), which requires a finer magnesium powder to sustain a reaction. Redox reaction experiments using four different amounts of magnesium powder are performed. Each result may or may not be further reduced in a second step using three different magnesium powder amounts. Each of these results may or may not be further reduced in a third step using three different amounts of magnesium powder.

(a) How many experiments are possible?

(b) If all outcomes are equally likely, what is the probability that the best result is obtained from an experiment that uses all three steps?

(c) Does the result in part (b) change if five or six or seven different amounts are used in the first step? Explain.